Comp/Phys/APSc 715 Tensor: Glyphs, Traces, Surfaces, Etc. 2/27/2014 - - PDF document

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2/27/2014 Comp/Phys/APSc 715 Tensor: Glyphs, Traces, Surfaces, Etc. 2/27/2014 Tensors Comp/Phys/APSc 715 Taylor 1 Preview Videos Vis2006: nlcglyph.mov Tensor glyph design Stress Tensor visualization for implant 2/27/2014 Tensors

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Tensor: Glyphs, Traces, Surfaces, Etc.

Comp/Phys/APSc 715

2/27/2014 Tensors 1 Comp/Phys/APSc 715 Taylor

Preview Videos

  • Vis2006: nlcglyph.mov

– Tensor glyph design

  • Stress Tensor visualization for implant

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Tensor Fields

  • One view: Mapping of input vectors to output vectors

– Stress (x,y,z) to strain (x,y,z): force to deformation

  • Another view: NxN matrix for N-space (3x3 for 3-space)
  • Subset: Symmetric second-order tensor fields

– Can be viewed as anisotropic ellipsoids – Three orthogonal Eigenvectors show directions – Associated Eigenvalues tell how much expansion/contraction along each vector – Largest “major” Eigenvalue, then middle and smallest “minor”

  • Subset: Rotation fields

– Spin at each location in space

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Tensor Questions

  • Is the tensor anisotropic in a specific area?
  • Where is the tensor sheet-like, cigar-like?
  • Where would water go from here?
  • Where are the most severe rotations?
  • What strain effect would stress have?
  • Does this technique work for 3D?

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Classes of Techniques

  • Glyphs
  • Stream Indicators
  • Hue and texture
  • Deformed Surfaces
  • Computer finds traces, visualization shows
  • Techniques to show rotation fields
  • Haptic display

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Glyphs: Flow Probe

  • Velocity gradient tensor
  • Shear and Divergence

form parts of the deformation rate tensor

  • Willem de Leeuw thesis

Acceleration Shear Curvature Torsion/Rot Convergence

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Two-stroke Engine, Tornado

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Tubes and Flow Probes

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Overpowering Chartjunk

Symmetric Second-Order Stress Tensor

  • Bar shows length and

direction of largest eigenvector

  • Ellipse axes show relative size
  • f the two other eigenvectors
  • Haber, 1990

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Seismic Stress Tensor: Hedgehogs

  • Scheurmann, Frey, Hamann, Jeremic, Joy;
  • U. Kaiserslautern (1997+)
  • Deformation under load

– Green lines show compression – Red lines show tension – Tripod “hedgehog”

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Other Hedgehogs

  • Solid cylinder surrounds the principal cylinder
  • Cheng, Koh, Lee, Vidal, & Haber

– UIUC

  • Chall, Idaszak, & Baker

– NCSA

  • Vis 1990

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Second-Order Diffusion Tensor Mapped to Ellipses

14

Second-Order Diffusion

  • Diffusion within mouse spinal-chord tissues

– Anisotropic rate of diffusion in three dimensions – Three orthogonal eigenvectors in 3D – Non-negative eigenvalues

  • Visualized as ellipsoid where liquid would spread

– From a single starting point – At different rates along different eigenvectors

  • Features

– Matrix values at every point in space – Spheres represent isotropic diffusion – Larger ellipsoids represent faster diffusion

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Detail view of ellipses

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Diffusion Tensor Images

  • David Laidlaw, IEEE Visualization 1998

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Left: Diseased; Right: Healthy

18

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Deformation Rate Tensor

  • Rate-of-Strain Tensor

Kirby, Marmanis, & Laidlaw; IEEE Vis 1999

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Other Iconic/Glyph Techniques

  • Post, Walsum, Post; Delft: Silver; Rutgers

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SLIDE 8

2/27/2014 8 Superellipsoids for Real Symmetric Traceless Tensors

  • T.J. Jankun-Kelly, Vis 2006

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Superellipsoids for Real Symmetric Traceless Tensors

  • T.J. Jankun-Kelly, Vis 2006
  • Nematic Liquid-Crystal

states drive glyph form

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Superellipsoids for Real Symmetric Traceless Tensors

  • T.J. Jankun-Kelly, Vis 2006

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2/27/2014 9 Superquadric Glyphs for Symmetric Second-Order Tensors

  • Thomas Schulz, Gordon Kindlemann; TVCG 2010

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Subsets of superquadric shapes are selected to form the base shapes. Coloration distinguishes geometrically-similar glyphs from different regions.

Superquadric Glyphs for Symmetric Second-Order Tensors

  • Thomas Schulz, Gordon Kindlemann; TVCG 2010

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Technique applied to the Hessian of the Laplacian zero-crossings describing the surface geometry of an earlobe

Glyphs: What are they good for?

  • Is the tensor anisotropic in a specific area?
  • Where is the tensor sheet-like, cigar-like?
  • Where would water go from here?
  • Where are the most severe rotations?
  • What strain effect would stress have?
  • Does this technique work for 3D?

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SLIDE 10

2/27/2014 10 Stream Indicators: Seismic Stress Tensor: Hyperstreamlines

  • Technique by Delmarcelle

– Tube along eigenvector – Widths based on others

  • Can follow any

– Major (shown here) follows largest – Medium and minor follow the other two

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Seismic Stress Tensor: Hyperstreamlines

  • Minor Hyperstreamlines for 2-point load

– Compression is negative

  • Hue based on magnitude

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Momentum Flux Density Tensor

  • Flow past a hemispherical cylinder
  • Shows flow along major eigenvector
  • Colored by difference in major eigenvalue

compared to the other two

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Streamballs Simplest

  • Can advect along eigenvector like hyperstreamline
  • Color similarly
  • Brill, et. al.

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Streamballs Variety

  • Can change connectivity, color, texture, microgeometry
  • Brill, et. al.

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Stream Indicators: What are they good for?

  • Is the tensor anisotropic in a specific area?
  • Where is the tensor sheet-like, cigar-like?
  • Where would water go from here?
  • Where are the most severe rotations?
  • What strain effect would stress have?
  • Does this technique work for 3D?

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Hue and Texture: Symmetric, Second- Order Tensor Fields

  • Delmarcelle & Hesselink
  • Vector flow by texture
  • Hue by magnitude of

largest compressive eigenvector

  • Dots show degenerate

points (>1 eigenvector parallel)

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Rainbow colormap

Symmetric, Second-Order Tensor Fields

  • Delmarcelle & Hesselink
  • Vector flow by texture
  • Hue by magnitude of

largest compressive eigenvector

  • Dots show degenerate

points (>1 eigenvector parallel)

  • Lines separate field into

topological regions

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Strain-Rate Tensor

  • Sigfridsson, Ebbers, Heiberg, & Wigstrom, Vis 2002.

Noise blurred by eigenvalue Larger values blur more Relative values only (normalized) L1 > L2 > L3 Color by degree of anisotropy R = (L1 – L2) / L1 (Linear) G = (L2 – L3) / L1 (Planar) B = L3 / L1 (Isotropic) Glyph shows zoom-in to planar region

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Occlusion and confusion

Fiber Stippling for Probabilistic Tracts

  • Goldau, Wiebel, et. al. VisBio 2011

– Stipple shape controlled by fiber properties – Different fibers shown by color, to view interleave

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Deformation of Noise Texture

  • Zheng and Pang, Vis2003, HyperLIC
  • Start with a uniform 2D/3D noise texture
  • Blur (flow) texture

– Along eigenvectors – Blurs where large & isotropic – LIC where anisotropic

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Deformation of Noise Texture

  • Zheng and Pang, Vis2003, HyperLIC
  • In 3D, opacity comes from anisotropy

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Hue and Texture: What are they good for?

  • Is the tensor anisotropic in a specific area?
  • Where is the tensor sheet-like, cigar-like?
  • Where would water go from here?
  • Where are the most severe rotations?
  • What strain effect would stress have?
  • Does this technique work for 3D?

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SLIDE 15

2/27/2014 15 Deformed Surfaces: Point-Load Stress Tensor

  • Boring and Pang
  • Deformation of sheet

– Exaggerated – Colored by magnitude

  • Minor hyperstreamlines

– Colored by magnitude

  • Insets:

– Lateral strain – Normal strain

  • Show the movie

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Delta-Wing Rate-of-Strain

  • Boring & Pang
  • Surface Deformation
  • Show Movie

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Cylindrical Cap and Flow

  • Boring & Pang
  • Deformation by

– Rate of strain – Normal component only – Extrusions = tensile – Depressions = compressive

  • Show Movie

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Zheng and Pang, Vis 2002

  • Deformation due to load

– Single Point Load – Opaque Surfaces – Colored by remaining tensor magnitude

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Severe occlusion

Zheng and Pang, Vis 2002

  • Deformation due to load

– Single Point Load – Transparent volumes – Colored by initial tensor magnitude

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Lack of occlusion

Zheng and Pang, Vis 2002

  • Deformation due to load

– Single Point Load – Wireframe grid – Colored by initial tensor magnitude

  • Viewed from the back

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Deformation of Rectangle

  • http://www.cs.auckland.ac.nz/~burkhard/PhD/img12.html
  • Cube coordinates displaced by vector data

– Second torsional mode of vibration for an object

  • Scalar offset mapped to double-ended color

– Red moves along surface normal – Black is little or no motion in direction of normal – Blue moves opposite surface normal

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Deformation of Shape

  • http://146.134.8.133/femtools/img/2ved04.gif
  • Advect shape by field
  • Shows strain
  • Could animate
  • 2D or 3D shape
  • Here, color nominal

– Original vs. deformed shape

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Deformation of Shape

  • Bender et. al. IEEE Transactions on Vis. &
  • Comp. Gfx., Vol 6. No. 1. 2000. Pp. 8-23

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Deformation of Shape

  • Bender et. al. IEEE Transactions on Vis. &
  • Comp. Gfx., Vol 6. No. 1. 2000. Pp. 8-23

Vibrating Shaft

52

Streamballs as Surfaces

  • Can deform like surfaces
  • Color similarly
  • Brill, et. al.

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Deformed Surfaces: What are they good for?

  • Is the tensor anisotropic in a specific area?
  • Where is the tensor sheet-like, cigar-like?
  • Where would water go from here?
  • Where are the most severe rotations?
  • What strain effect would stress have?
  • Does this technique work for 3D?

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Computed: Streamtubes and Streamsurfaces

  • Tubes

– Flow mostly along line – Along principal direction of diffusion – Cross-section is ellipse – Saturation shows anisotropy

  • Surfaces

– Where diffusion larger in 2 directions than 3rd – Perpendicular to slowest – Saturation shows anisotropy

  • Annotated landmarks

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Streamtubes/Surfaces Side View

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Getting Into the Data

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White-Matter Fiber Tracing

  • Zhukov & Barr, Caltech; Vis 2002

We applied the method to human brain diffusion tensor DT-MRI data and recovered identifiable anatomical structures that correspond to the white matter brain-fiber pathways. In this paper we develop a new technique for tracing anatomical fibers from 3D diffusion tensor fields. The technique extracts salient tensor features using a local regularizing technique that allows the algorithm to cross noisy regions and bridge gaps in the data.

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White-Matter Fiber Tracing

  • Zhukov & Barr

– Caltech – Vis 2002

  • Trace streamlines

– Along major Eigenvector

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White-Matter Fiber Tracing

  • Zhukov & Barr, Caltech; Vis 2002
  • Streamlines along major eigenvector

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White-Matter Fiber Tracing

  • Zhukov & Barr, Caltech; Vis 2002

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Adding Halos

  • Interactive volume rendering of thin thread

structures within multivalued scientific data sets

– Wenger, Keefe, Zhang & Laidlaw 2004

  • Left: no halos, middle: halos, right: halos

shifted away from the viewer

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Multi-source Streamlines

  • Vis 2005, Blaas et. al.

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In-Vivo Tractography

  • Basser et. al. 2002

– Volume render fiber-tract density

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In-Vivo Tractography

  • Basser et. al. 2002

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SLIDE 23

2/27/2014 23 Computed Tubes and Surfaces: What are they good for?

  • Is the tensor anisotropic in a specific area?
  • Where is the tensor sheet-like, cigar-like?
  • Where would water go from here?
  • Where are the most severe rotations?
  • What strain effect would stress have?
  • Does this technique work for 3D?

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Rotation Field

  • Livingston, Vis ’97
  • Tracker Orientation Errors
  • Cube is tracker source
  • Spinning colored tuftes

– Red, green, and blue sides – Animate

  • Spin around axis
  • Speed by error magnitude
  • Shows subtle differences

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Rotation Field

  • Livingston, Vis ’97
  • Tracker Orientation Errors
  • Cube is tracker source
  • Orienting axes

– Rotated by error amount – Best when fly-through – Animate to shift from starting orientation to final

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Rotation Field

  • Livingston, Vis ’97
  • Tracker Orientation Errors
  • Cube is tracker source
  • Axis streamlines

– Not hyperstreamlines (along eigenvectors) – Integrate along the rotated coordinate axis – Tile adjacent ones to provide strips

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Combined 2D Techniques

  • Asymmetric Tensor Field Vis for Surfaces

– Chen, Palke, et. al.; TVCG 2011

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Combined 2D Techniques

  • Asymmetric Tensor Field Vis for Surfaces

– Chen, Palke, et. al.; TVCG 2011

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Combined Display

  • www-sop.inria.fr/epidaure/personnel/ayache/ayache.html
  • 2/27/2014 Tensors

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2006 images, show with Quicktime

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Combined Display

  • www-sop.inria.fr/epidaure/personnel/ayache/ayache.html

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2006 images, show with VLC

Haptic Diffusion Tensor Display

  • A Constraint-Based Technique for Haptic Volume Exploration: Vis 2003;

Ikits, Brederson, Hansen, Johnson

  • Anisotropic drag

– along Eigenvectors – by Eigenvalues

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Summary (From 2003)

  • Is it isotropic? Ellipsoids, Stream ind (color compares 2),

Hue&Tex in 2D, Deformation(color)

  • Sheet or cigar: Ellipsoids, Stream is hard, others not.
  • Where would water diffuse? Stream for 1, hue&tex, Deform
  • Where severe rotation? FlowProbe, Flowtubes, Streamballs

for surface

  • What strain caused by stress? Glyph, Deformation
  • Does it work for 3D? Glyphs have occlusion trouble, tricks let

hue&text, great care or 2D subsets for deformations

  • All: “Computed” depends on what you computed

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Summary (from 2002)

E f I s TP a Isotropic/anisotropic tensor field? E I s TP Where is it sheet-like, where cigar-like? H P e f I S W TP A Where would water go from here? h P W a R Where are the most severe rotations? I S W A What strain effect does stress cause? p I S W A R Does it work in 3D?

(H)ue/velocity, Flow (P)robe, (E)llipsoids, (F)lat/2D ellipses, (I)cons (includes P,E,F), Hyper(S)treamlines, (W)arped surface, (TP) Tubes and Planes, (A)dvect shape, (R)otation (anim. axis)

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Other References

  • Ding, Gore, & Anderson, “Case Study: Reconstruction,

Visualization and Quantification of Neuronal Fiber Pathways,” IEEE Vis 2001. pp. 453-456.

  • Lavin & Levy, “Singularities in Nonuniform Tensor Fields,” IEEE

Vis 1998. pp. 59-66.

  • IEEE Visualization 2002 has a whole session on tensor field

visualization, of which only one paper is presented.

  • http://www.cs.auckland.ac.nz/~burkhard/PhD/introduction.ht

ml

  • Delmarcelle and Hesselink, “Visualization of second order

tensor fields and matrix data,” IEEE CG&A 13(4):25-33, July

  • 1993. Hyperstreamlines.

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Other References

  • Dickinson, “A unified approach to the design of visualization

software for the analysis of field problems,” SPIE Three- dimensional visualization and display technologies vol 1083, pages 173-180. 1989. Tensor field lines.

  • Kindlemann & Weinstein, Hue-balls paper, Vis ’99.
  • Nielson G., H. Hagen, and H. Mueller (eds.): Scientific

Visualization - Overview, Methodologies and Techniques, IEEE Computer Society Press, pp. 357--371, (1997).

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Credits

  • Second-Order Diffusion Tensor of MRI images: David Laidlaw, Eric T.

Ahrens, Carol Readhead, Celia F. Brosnan, and Scott E. Fraser, Siggraph Technical Slide Set, 1997.

  • Diffusion tensor images on spinal chords: David Laidlaw, David

Kremers, Eric T. Ahrens, and Matthew J. Avalos, Siggraph Technical Slide Set, 1998.

  • Diffusion tensor image on airfoil flow: David Laidlaw, Matthew J.

Avalos and David Kremers, Siggraph Technical Slide Set, 1998.

  • Flow Probe: Willem de Leeuw and van Wijk, “A probe for local flow

field visualization,” Vis 93, 39-45.

  • Point-Load Stress Tensor, Delta-Wing Rate-of-Strain, Cylindrical Cap

and Flow: Boring and Pang, IEEE Vis ’98

  • Rotation Fields: Livingston, “Visualization of rotation fields,” IEEE Vis

97, 491-494.

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Credits

  • Bar-and-ellipse: R.B. Haber. Visualization techniques for engineering
  • mechanics. Computing Systems in Engineering, 1(1):37–50, 1990.
  • Flow Probe, Two-stroke engine, Tornado: Willem de Leeuw’s thesis

provides good background and a detailed description of the flow probe: http://www.cwi.nl/~wimc/psgz/these.pdf

  • “An immersive virtual environment for dt-mri volume visualization

applications: a case study” Song Zhang, Cagatay Demiralp, Daniel Keefe, Marco DaSilva, Benjamin D. Greenberg, Peter J. Basser, Carlo Pierpaoli, E.

  • A. Chiocca, T. S. Deisboeck, and David H. Laidlaw. In Proceedings of IEEE

Visualization 2001, pages 437–440, October 2001.

  • Seismic Stress Tensors: Scheurmann, Frey, Hamann, Jeremic, Joy; U.

Kaiserslautem (1997+).

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Credits

  • Momentum Flux Density Tensor: Delmarcelle & Hesselink, 1993.
  • Symmetric, Second-Order Tensor Fields: Delmarcelle & Hesselkink 1994,

IEEE Vis. pp. 140-147.

  • Streamball techniques: Brill, Hagen, Rodrian, Djatschin, and Klimenko,

“Streamball Techniques for Flow Visualization,” IEEE Vis 1994. pp. 225-231.

  • Iconic Techniques: Reprinted from IEEE Vis '95, “Iconic Techniques for

Feature Visualization,” pp. 288-295.

  • Other Hedgehogs, "Visualization Idioms: A Conceptual Model for Scientific

Visualization Systems". Chen Sheng, Hyun Koh,Hae Sung Lee, Creto Vidal, and Robert Haber, Steve Chall, Ray Idaszak, and Polly Baker, NSCA.

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Credits

  • White-Matter Fiber Tracing: Leonid E. Zhukov and Alan H. Barr, California

Institute of Technology, “Oriented Tensor Reconstruction: Tracing Neural Pathways from Diffusion Tensor MRI,” IEEE Vis 2002.

  • In Vivo Tractography: Basser, Pajevic, Pierpaoli, Aldroubi, “Fiber Tract

Following in the Human Brain Using DT-MRI Data,” IEICE Trans. Inf. & Syst. Vol E85-D, No. 1. Jan 2002. pp. 15-21.

  • Other Iconic Techniques, Tubes and Flow Probes, Post, et. al., “Iconic

techniques for feature visualization,” Vis 95, 288-295.

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